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With the DOJ headaches in the rearview mirror, is now a good time to buy Citigroup?

DOJ settlementNo doubt, the big take-away from Citigroup's second quarter results was the settlement with the Department of Justice.

While Citigroup originally was prepared to throw away $4 billion, Citigroup announced, as part of its second quarter earnings release, that it has reached a settlement over soured mortgage-backed securities and collateralized debt obligations with the Department of Justice for $7 billion.

The $7 billion settlement contains two elements: $4.5 billion are part of a civil penalty being paid to the Department of Justice, state attorneys general and the Federal Deposit Insurance Corporation. Another $2.5 billion will be paid in consumer relief.

The settlement affected Citigroup's second quarter results with an $3.7 billion after-tax charge.

Second quarter resultsOther than the settlement impact on financial results, Citigroup's earnings release contained little surprises and the bank is still facing a challenging operating environment with non-existent or weak revenue growth.

Citigroup reported adjusted earnings of $1.24 per diluted share which compares against $1.25 per diluted share last year and against analyst estimates of $1.05 per share.

More important than any particular revenue or earnings number, however, are underlying trends in capital strength or book value growth in order to gauge a feeling as to how Citigroup's business has been developing lately.

Solid trends in building capital and book valueIf often helps to take a step back from the developments in any particular quarter, especially if it is boring, and look at the progress a bank has made of a series of quarters in regaining strength and setting the foundation for future growth.

Citigroup's capital ratios, for instance, have gradually been improving over the last two years. Its Tier 1 Common Basel III ratio has increased from 7.9% in the second quarter of 2012 to 10.6% in the most recent quarter making Citigroup much more resilient to any shock in the banking sector or to an economic contraction.

Over the same time, Citigroup's book value only declined one time sequentially, in the fourth quarter of 2012, but has increased ever since.

Citigroup's tangible book value per share currently stands at $56.89 reflecting a 1% sequential increase despite the mortgage settlement and a 7% year-over-year increase.

Moving forwardThough Citigroup's results didn't contain any specific nuggets, that would either justify the bull or the bear case, Citigroup's long-term value proposition is compelling.

First off, the settlement allows the bank to concentrate on moving forward and, specifically, grow its strong international consumer banking franchise.

Secondly, investors are likely to reassess Citigroup's long-term value proposition now that a major risk has been mitigated.

Long-term value propositionJ.P. Morgan(NYSE:JPM) settled with the Department of Justice over the same allegations that hit Citigroup for a total consideration of $13 billion last year. And Bank of America(NYSE:BAC), which is probably about to announce a similar deal with the DOJ any day, might shell out somewhere in the $15 billion region to end the probe into its mortgage practices.

Even though J.P. Morgan was hit and Bank of America is about to get hit with multi-billion dollar civil penalties, both companies trade at a premium to tangible book value while Citigroup still trades at a discount.

Evaluated on their price to tangible book value ratios, Citigroup is still the cheapest company of all domestic, large-cap banking franchises and has a lot of potential to catch up the valuation of its immediate peers.

Citigroup's current discount to tangible book value is 13% while both Bank of America and J.P. Morgan already trade at premiums to tangible book value of 18% and 45% respectively.

In the long-run, all big banks should do reasonably well as essential pillars of the U.S. financial system. This is especially true if the housing market continues to recover and the mortgage business experiences tailwinds.

The Foolish Bottom LineCitigroup's settlement with the DOJ is a milestone achievement and should allow the bank to focus on growth. The settlement is also a relief for shareholders who pushed Citigroup's stock way too low over the last couple of months as evidenced by a comparatively low tangible book value multiple.

Though Citigroup's earnings didn't justify an outburst of euphoria, the company is on the right way to build its grow its business. Consistent increases in its book value per share and improving capital ratios only add to the compelling long-term value proposition of Citigroup.